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On the Persistence of Abnormal Returns: an Analysis Using Structural Equation

Models Albert Satorra

Universitat Pompeu Fabra. Barcelona

&

Juan Carlos Bou

Universitat Jaume I. Castelló

Bou and Satorra (2007), SMJ

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This talk

• Introduction: permanent and transitory components of profits (ROA)

• Data & model • Substantive hypotheses• SEM: one- and two-level analyses • Variance decomposition of profits:

– temporary vs permanent– Industry vs firm levels

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Introduction• actual profit rates differ widely across firms, both between and within industries.

• Some firms show what can be regarded as ``abnormal returns'', i.e. returns that deviate substantially from the mean return level of all the firms.

• According to economic theory, in a ``competitive market'' these differences should disappear as the time passes.

• How much evidence exists of the persistence of abnormal returns, or how much variation of the returns can be attributed to permanent and time-vanishing components

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Data

• Initial sample: 5000 Spanish firms (excluding finance and public companies)

• Screened database: 4931 firms• Financial Profit data were collected for each

firm (Return On Assets, ROA)• 6 Time Period: 1995 – 2000• Firms were classified by 4-digit SIC code• Number of Industries: 342 (quasi average

number of firms: 14.28)

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ROA across time

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Scatterplots and correlations

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Summary statistics   

Table 1: Descriptive statistics and intercorrelations Mean S.D. 1 2 3 4 5 6 1. ROA 95 7.745 9.396 1.000 2. ROA 96 7.558 8.886 0.671 1.000 3. ROA 97 7.739 8.852 0.567 0.727 1.000 4. ROA 98 8.037 8.928 0.460 0.576 0.727 1.000 5. ROA 99 8.134 8.868 0.403 0.489 0.616 0.758 1.000 6. ROA 00 7.982 8.960 0.365 0.420 0.515 0.605 0.727 1.000

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Intraclass Correlations (within industry)

Variable Correlation

Y1 0.070 Y2 0.082 Y3 0.085 Y4 0.107 Y5 0.121 Y6 0.088

Seminario Modelos de Ecuaciones Estructurales. Universitat Jaume I, Castelló, 12 y 13 de Julio de 2004Albert Satorra & Juan Carlos Bou

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Anderson and Hsiao's State-Dependence model (1982)Using SEM, this is Kenny and Zautra's (1985) Trait-State-Error model. Here we extend these models to two-level data

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A1 A2 A3 A4 A5 A6

1 1 1 1 1 1

D1 D2 D3 D4 D5 D6

ROS95 ROS96 ROS97 ROS98 ROS99 ROS00

P

1 1 1 1 1 1

E1 E2 E3 E4 E5 E6

one-level SEM

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Test statistics

See Satorra (1982) for asymptotic robustness of these normal-theory test statistics, and Satorra and Bentler (1994) for robust versions of these statistics.

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Estimates for one-level model

Chi2 goodness-of-fit test = 17.45, df = 10, p-value = 0.095

All the variances of the D’s are equal except for D of 1998 (that has greater variance, 28.14) . The variances of the E’s are unrestricted. Variance of A1 subject to a non-linear restriction.

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Roughly: 65 25 10 %

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Permanent component

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TWO-LEVEL SEM:

* INDUSTRY level:

* FIRM level:

AI1 AI2 AI3 AI4 AI5 AI6

1 1 1 1 1 1

DI1 DI2 DI3 DI4 DI5 DI6

0 0 0 0 0

ROA95 ROA96 ROA97 ROA98 ROA99 ROA00

IP

1 1 1 1 1 1

E1 E2 E3 E4 E5 E6

AF1 AF2 AF3 AF4 AF5 AF6

1 1 1 1 1 1

DF1 DF2 DF3 DF4 DF5 DF6

1 1 1 1 1

ROA95 ROA96 ROA97 ROA98 ROA99 ROA00

FP

1 1 1 1 1 1

E1 E2 E3 E4 E5 E6

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Two-level variation

zgi := (Yig1, Yig2, ...., YigT)’

Firm: i=1,2, ..., ng; Industry: g=1, 2, ..., GTime: t=1,2, ..., T

zgi = + ug + vig

level 1: vig ~ 1 1 ()

level 2: ug ~ 2 2 ()

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See Muthén and Satorra, 1995

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... in the balanced case

See Muthén and Satorra, 1995

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TESTS OF MODEL FIT

Chi-Square Test of Model Fit

Value 32.727* Degrees of Freedom 31 P-Value 0.3821 Scaling Correction Factor 2.411 for MLM

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Firm level Industry level

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Conclusions: two-level model • There exist significant permanent and temporary profit differences at industry

and firm level

INSERT TABLE 5

• Industry effects < Firm effects– Industry permanent differences < firm permanent differences– Industry temporary differences < firm temporary differences

• The same “memory” parameter, common .72 , of the transitory component of firm and industry levels

Var(P)

Var(A)

(noise, Var(D), is not included in this variance decomposition)